Source localization for EEG and MEG

1. Source localization for EEG and MEG Methods for Dummies 2006 FIL Bahador Bahrami

2. Before we start … • SPM5 and source localization: • On-going work in progress • MFD and source localization: • This is the first on this topic • Main references for this talk: • Jeremie Mattout’s slides from SPM course • Slotnick S.D. chapter in Todd Handy’s ERP handbook • Rimona Weil’s wonderful help (thanks Rimona!)

3. Outline • Theoretical • Source localization stated as a problem • Solution to the problem and their limitations • Practical* • How to prepare data • Which buttons to press • What to avoid • What to expect * Subject to change along with the development of SPM 5

4. Source localization as a problem

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7. + - + - Any field potential vector could be consistent with an infinite number of possible dipoles The possibilities only increase with tri-poles and quadra-poles

8. ERP and MEG give us

9. + - And source localization aims to infer among

10. + - + - How do we know which one is correct? We can’t. There is no correct answer. Source localization is an ILL-DEFINED PROBLEM We can only see which one is better Can we find the best answer? Only among the alternatives that you have considered.

11. MEG sensor location MEG data HUNTING for best possible solution Step ONE: How does your data look like? Source Reconstruction Registration

12. If then If then If then If HUNTING for best possible solution Step Two then FORWARD MODEL And on and on and on and …

13. HUNTING for best possible solution Forward Model Experimental DATA Inverse Solution Which forward solutions fit the DATA better (less error)?

14. error iteration HUNTING for best possible solution Forward DATA Inverse Solution Iterative Process Until solution stops getting better (error stabilises)

15. Components of the source reconstruction process Source model ‘ECD’ ‘Imaging’ Forward model Registration Inverse method Data Anatomy

16. Recipe for Source localization in SPM5 • Ingredients • MEG converter has given you • .MAT data file (contains experimental data) • sensloc file (sensors locations) • sensorient (sensors orientations) • fidloc(fiducial locations in MEG space) • fidloc in MRI space (we will see shortly) • Structural T1 MRI scan All in the same folder

17. X Y Z Nasion Nasion Nasion X Y Z Left Tragus Left Tragus Left Tragus X Y Z Right Tragus Right Tragus Right Tragus fidloc in MRI space Get these using SPM Display button Save it as a MAT file in the same directory as the data

19. Components of the source reconstruction process Forward model Inverse solution Source model Registration

20. Source model

21. Source model Compute transformation T Individual MRI Templates Apply inverse transformation T-1 Individual mesh functions output • Individual MRI • Template mesh • spatial normalization into MNI template • inverted transformation applied to the template mesh • individual mesh

26. Scalp Mesh iskull mesh

27. Components of the source reconstruction process Registration

28. fiducials fiducials Rigid transformation (R,t) Individual sensor space Individual MRI space Registration input functions output • sensor locations • fiducial locations • (in both sensor & MRI space) • individual MRI • registration of the EEG/MEG data into individual MRI space • registrated data • rigid transformation

32. Forward model

33. Model of the head tissue properties Individual MRI space Foward model Compute for each dipole + K n Forward operator functions input output • single sphere • three spheres • overlapping spheres • realistic spheres • sensor locations • individual mesh • forward operator K BrainStorm

36. Inverse solution

37. 1 dipole source per location Y = KJ+ E [nxt] [nxt] [nxp] [pxt] : min( ||Y – KJ||2 + λf(J) ) J J Inverse solution (1) - General principles General Linear Model Cortical mesh n : number of sensors p : number of dipoles t : number of time samples Under-determined GLM ^ Regularized solution data fit priors

38. E1 ~ N(0,Ce) Y = KJ + E1 E2 ~ N(0,Cp) J = 0 + E2 Ce = 1.Qe1 + … + q.Qeq Cp = λ1.Qp1 + … + λk.Qpk Inverse solution (2) - Parametric empirical Bayes 2-level hierarchical model Gaussian variables with unknown variance Gaussian variables with unknown variance Sensor level Source level Linear parametrization of the variances Q: variance components (,λ): hyperparameters

39. Qe1 , … , Qeq + + Model M Qp1 , … , Qpk J K ,λ ^ J = CJKT[Ce + KCJ KT]-1Y Inverse solution (3) - Parametric empirical Bayes Bayesian inference on model parameters Inference on J and (,λ) Maximizing the log-evidence F = log( p(Y|M) ) =  log(p(Y|J,M) ) + log( p(J|M) )dJ data fit priors Expectation-Maximization (EM) E-step: maximizing F wrt J MAP estimate M-step: maximizing of F wrt (,λ) Ce + KCJKT = E[YYT] ReML estimate

40. p(Y|M1) p(Y|M2) B12 = Inverse solution (4) - Parametric empirical Bayes Bayesian model comparison Model evidence • Relevance of model M is quantified by its evidence p(Y|M) maximized by the EM scheme Model comparison • Two models M1 and M2 can be compared by the ratio of their evidence Bayes factor Model selection using a ‘Leaving-one-prior-out-strategy‘

41. ECD approach • iterative forward and inverse computation Inverse solution (5) - implementation input functions output • preprocessed data • - forward operator • individual mesh • priors • - compute the MAP estimate of J • compute the ReML estimate of (,λ) • interpolate into individual MRI voxel-space • inverse estimate • model evidence

42. error iteration HUNTING for best possible solution Forward DATA Inverse Solution Iterative Process Until solution stops getting better (error stabilises)

44. Types of Analysis • Evoked • The evoked response is a reproducible response which occurs after each stimulation and is phase-locked with the stimulus onset. • Induced • The induced response is usually characterized in the frequency domain and contrary to the evoked response, is not phased-locked with the stimulus onset. • The evoked response is obtained (on the scalp) as the stimulus or event-locked average over trials. This is then the input data for the 'evoked' case in source reconstruction. • One can also reconstruct the evoked power in some frequency band (over the time window), this is what is obtained when choosing 'both' in source reconstruction. Jeremie says: